Q: After battery replacement, car still won't start

Occasionally, before being able to drive, my car has to be jump-started. The battery was an old one, so I purchased a new one and installed it myself. So now the car surely has enough juice because all the seats, radio, and lights - all turn on. But the engine still won't run when I try starting my car. It makes a noise like it is Wanting to start, but it doesn’t. Like I said earlier, sometimes it will jump-start, but often it won't jump-start with cables. I'm thinking this might be the starter, alternator, catalytic converter, or fuel lines. I would like to do the work myself. What is your diagnosis of this problem?